- #1

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## Homework Statement

lim x->1 (X^9 + x -2)/(x^4 + x -2)

I know how to do this using L'Hopitals Rule and I get 2

## Homework Equations

(1+b)^n = 1 + bn + n(n-1)b^2/2! + n(n-1)(n-2)b^3/3! ....

## The Attempt at a Solution

Let x = h+1

x -> 1

h -> 0

lim h->0 (h+1)^9 + h-1/(h+1)^4+h-1

lim h->0 h^9 (1+1/h)^9 +h-1/h^4(1+1/h)^4 +h-1

Binomial theorem:

(1+1/h)^9 = 1 +9/h +36/h^2 + 84/h^3 ...

(1+1/h)^4 = 1 +4/h + 6/h^2 + 4/h^3 ...

lim h->0 h^9(1 +9/h +36/h^2 + 84/h^3 ...) +h-1/h^4(1 +4/h + 6/h^2 + 4/h^3 ...) +h-1

This is stil ∞.0 right?

I tried to get rid of the +h-1 at the end by doing

h^7(h^2 +10h +35 +84/h...)/h^2(h^2+5h+5+4/h...)

but then you get ∞.∞